![\bf f(x)=(x-6)e^{-3x}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}=1\cdot e^{-3x}+(x-6)-3e^{-3x}\implies \cfrac{dy}{dx}=e^{-3x}[1-3(x-6)] \\\\\\ \cfrac{dy}{dx}=e^{-3x}(19-3x)\implies \cfrac{dy}{dx}=\cfrac{19-3x}{e^{3x}}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3D%28x-6%29e%5E%7B-3x%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3D1%5Ccdot%20e%5E%7B-3x%7D%2B%28x-6%29-3e%5E%7B-3x%7D%5Cimplies%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3De%5E%7B-3x%7D%5B1-3%28x-6%29%5D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3De%5E%7B-3x%7D%2819-3x%29%5Cimplies%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7B19-3x%7D%7Be%5E%7B3x%7D%7D)
set the derivative to 0, solve for "x" to get any critical points
keep in mind, setting the denominator to 0, also gives us critical points, however, in this case, the denominator will never be 0, so... no critical points from there
there's only 1 critical point anyway, and do a first-derivative test on it, check a number before it and after it, to see what sign the derivative has, and thus, whether the graph is going up or down, to check for any extrema
Answer:
c and d
Step-by-step explanation:
3 x 3 = 1
25/25 = 1
any value multiplied by 1 remains itself
Answer:
Option A is correct.
Step-by-step explanation:
As we see the graph, we can say that the correct statement is :
A.)All repairs requiring 1 hour or less have the same labor cost. We can see that the coat from 0 hours to 1 hour is $50. So, the number of hours falling in this range has the same repairing cost.
B.) Labor costs the same no matter how many hours are used for a repair. This is wrong as the graph is increasing after 1 hour.
C.) Labor costs for a repair are more expensive as the number of hours increases. This is wrong as the hours are increasing from 0.25 to 0.5 then to 0.75 but they all have the same cost.
D.)There is no cost of labor for a repair requiring less than 1 hour. This is also wrong. The cost is $50.
For question 1
x^7
for question 2
h^9
3xy(x+4)(2y+7)(xy+1) is what I got
